文章基本信息

标题：A generalized stochastic Markov model describing interactive gating of ion channels.
作者：Marsh, Daniel
期刊名称：Transactions of the Missouri Academy of Science
印刷版ISSN：0544-540X
出版年度：2005
期号：January
语种：English
出版社：Missouri Academy of Science
摘要：Patch-clamp is a powerful technique to study ion channel currents. In general, patch clamp recordings from membrane patches containing multiple channels exhibit an independent gating behavior consistent with binomial probability distribution. However in some preparations, observations suggest a cooperative gating behavior among channels that does not follow a binomial distribution. To understand this, consider a system of two-channels. Let the probability of observing 2-closed, 1-open, and 2-open current levels be [A.sub.0], [A.sub.1], and [A.sub.2]. For independently gating channels, the ratios [A.sub.0]: [A.sub.1]: [A.sub.2] = 1: 2r: r2, where r is the ratio of open to closed probability of a single channel. Previously, a model based on steady-state probabilities has been formulated to describe cooperative ion channel gating with two additional parameters, rc and ro, representing closed-closed and open-open interactions. This gives [A.sub.0]: [A.sub.1]: [A.sub.2] = (1 + rc): 2r: [r.sup.2](1 + [r.sub.0]). This paper extends the previous model by enumerating all possible combinations of states in an interacting N-channel system with one additional parameter, rb, denoting closed-open interactions. For two channels, this model yields [A.sub.0]: [A.sub.1]: [A.sub.2] = (1 + rc): 2r(1 + rb): [r.sup.2](1 + [r.sub.0].). This model provides exact expressions for three- and four- channels system, and a procedure to analyze an arbitrary number of channels. Ion channels are major drug targets, and the scientific community and the pharmaceutical industry are substantially invested in the endeavor to understand them. This mathematical model will facilitate quantitative analysis and interpretation of cooperative ion channel gating in living systems.
关键词：Ion channels

A generalized stochastic Markov model describing interactive gating of ion channels.

Marsh, Daniel

Patch-clamp is a powerful technique to study ion channel currents. In general, patch clamp recordings from membrane patches containing multiple channels exhibit an independent gating behavior consistent with binomial probability distribution. However in some preparations, observations suggest a cooperative gating behavior among channels that does not follow a binomial distribution. To understand this, consider a system of two-channels. Let the probability of observing 2-closed, 1-open, and 2-open current levels be [A.sub.0], [A.sub.1], and [A.sub.2]. For independently gating channels, the ratios [A.sub.0]: [A.sub.1]: [A.sub.2] = 1: 2r: r2, where r is the ratio of open to closed probability of a single channel. Previously, a model based on steady-state probabilities has been formulated to describe cooperative ion channel gating with two additional parameters, rc and ro, representing closed-closed and open-open interactions. This gives [A.sub.0]: [A.sub.1]: [A.sub.2] = (1 + rc): 2r: [r.sup.2](1 + [r.sub.0]). This paper extends the previous model by enumerating all possible combinations of states in an interacting N-channel system with one additional parameter, rb, denoting closed-open interactions. For two channels, this model yields [A.sub.0]: [A.sub.1]: [A.sub.2] = (1 + rc): 2r(1 + rb): [r.sup.2](1 + [r.sub.0].). This model provides exact expressions for three- and four- channels system, and a procedure to analyze an arbitrary number of channels. Ion channels are major drug targets, and the scientific community and the pharmaceutical industry are substantially invested in the endeavor to understand them. This mathematical model will facilitate quantitative analysis and interpretation of cooperative ion channel gating in living systems.

* Summers, M.W. and K. Manivannan. Department of Physics, Astronomy and Materials Sciences, Southwest Missouri State University.